Guerrero bagged his first of the night on 63 minutes, but Juan Fernando Arango brought Venezuela back into the match 13 minutes from time with a crisp finish. Guerrero had the final say, however, completing his treble with two late strikes to move clear as the tournament's top scorer with five goals.
"We are happy to have clinched third place," Guerrero said. "We all fought hard for this and we knew we had a match like this in us."
Peru had the better of the opening exchanges, but could manage only two half-chances in the first 20 minutes, with Christian Ramos' downward header from a corner and Carlos Lobaton's dangerously flicked on free-kick both picked off by Venezuelan goalkeeper Renny Vega.
On 37 minutes Peru went close again when Rinaldo Cruzado's neat one-two with Chiroque ended with the latter firing against the legs of the keeper. Venezuela pressured more as the half wore on, and Giancarlos Maldonado had a goal chalked off for offside on 29 minutes, while two minutes later the same player saw his cheeky back-heeled effort also ruled out after he strayed beyond the last man in the build-up.
Maldonado was in the thick of the action again on 34 minutes, nodding the ball down for Miku who turned his man before firing in a shot that produced a smart save from Raul Fernandez. But for all Venezuela's increasing pressure, it was Peru who found themselves ahead in the 42nd minute.
A quick break did the damage, Chiroque running at the last two defenders before picking out Guerrero, who squared the ball for Chiroque to knock home. And, Venezuela's hopes of drawing things level were hit just before the hour mark when they were reduced to ten men.
Rincon sees red again
Rincon, who missed his side's semi-final defeat due to a red card in the quarter-final win over Chile, was again dismissed in the 58th minute for a challenge on Carlos Lobaton. It took just five minutes for Peru to take advantage of Rincon's exit. Guerrero combined well with Chiroque, who lashed high into the net to register his third goal of the tournament.
Venezuela got back into the match with 12 minutes remaining when Yoandry Orozco's superb 20-yard through ball was collected by Arango, who kept his cool to convert sweetly with the outside of his left boot.
Minutes later Arango's free-kick was poorly dealt with by Fernandez, whose parry went back into the danger zone only for Gabriel Cichero to blaze wide with the goal gaping. And, Cichero's miss was punished in the 90th minute when Guerrero was played in, the striker taking a touch before burying the ball precisely in the opposite corner.
The Venezuelan defence was run into the ground, and three minutes into stoppage time Guerrero netted his third after being played in by Luis Advincula, the goalscorer again showing a cool head as he tucked the ball home low into the net.